In Artificial Intelligence, analogy is used as a non exact reasoning technique to solve problems, for natural language processing, for learning classification rules, etc. This paper is interested in the analogical proportion, a simple form of the reasoning by analogy, and presents some of its uses in machine learning for NLP. The analogical proportion is a relation between four objects that expresses that the way to transform the first object into the second is the same as the way to transform the third in the fourth. We firstly give definitions about the general notion of analogical proportion between four objects. We give a special focus on objects structured as ordered and labeled trees, with an original definition of analogy based on optimal alignment. Secondly, we present two algorithms which deal with tree analogical matching and solving analogical equations between trees. We show their use in two applications : the learning of the syntactic tree (parsing) of a sentence and the generation of prosody for synthetic speech.